What is the answer to solvefor x,xe^{-2x}-2y=0 ?

The answer to solvefor x,xe^{-2x}-2y=0 is x=-(\W(-4y))/2

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solvefor x,xe^{-2x}-2y=0

solve for

x, x e^{- 2 x} - 2 y = 0

x = - \frac{W ( - 4 y )}{2}

Solution steps

x e^{- 2 x} - 2 y = 0

Prepare

x e^{- 2 x} - 2 y = 0

for Lambert form:

x e^{- 2 x} = 2 y

Rewrite the equation with

- 2 x = u

and

x = - \frac{u}{2}

(- \frac{u}{2}) e^{u} = 2 y

Rewrite

(- \frac{u}{2}) e^{u} = 2 y

in Lambert form:

e^{u} u = - 4 y

Solve

e^{u} u = - 4 y : u = W (- 4 y)

u = W (- 4 y)

Substitute back

u = - 2 x,

solve for

x

Solve

- 2 x = W (- 4 y) : x = - \frac{W ( - 4 y )}{2}

x = - \frac{W ( - 4 y )}{2}

3^{2 x - 1} = 8 1^{2 x - 4}

6 \cdot 2^{n - 1} = 49152

2 (3)^{x} = 34, lo g_{10} (x)

9 x 2 7^{x} = 27

a = 27.2 e^{0.031 t}

What is the answer to solvefor x,xe^{-2x}-2y=0 ?
The answer to solvefor x,xe^{-2x}-2y=0 is x=-(\W(-4y))/2